Coverdell ESAs have low contribution limits, and an income limit that may keep you from contributing at all. Currently, in order to contribute to an ESA at all, you and your spouse must make less than $220,000 per year (combined).
The annual contribution limit to an ESA is $2,000, and the contributions made to an ESA are not tax-deductible. These limits have not been adjusted for inflation in years, and these plans are quickly becoming obsolete.
Unlike a 529 plan, also, Coverdell limits are per-child, and are aggregated for all accounts opened on behalf of that child. If the grandparents have a Coverdell for the child, and they contribute $2,000 a year into it, the parents are not able to contribute to a Coverdell for that child in that year.
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